Question

Which of the following is a step in constructing a circle circumscribed about a triangle?

Construct the perpendicular bisectors of each side.

Construct the angle bisectors of each side.

Use a compass to locate the midpoint of each side.

Use a compass to locate the altitude of each side.

Answer 1

Well, I'll explain this as best I can. Awesome problem, BTW.
That's a crappy drawing. But I'll explain. You'd want to choose the first choice, and construct the perpendicular bisectors. If you draw a straight line from each of the triangles' vertices, you'll find that each line comes in contact with an opposite side and forms a 90 degree angle there. Those lines you drew would be the bisectors. If you drew three of those lines, you probably also saw that these bisectors all intersect at one point; the distance from that center point to each of the triangle's vertices is a circle's radius! Yeah baby, now we're cookin' with serious grease! I adjusted my compass's two points according to my figure, so that one point stood on the center of the triangle (which we found by locating the point at which the bisectors all intersected) and the other point, the pencil point, stood on one of the triangle's vertices. All I had to do now was rotate the compass a full 360 degrees, and boom! I got my circumscribed circle.

That's a fun problem. Good luck! ^_^

Answer 2

Hm. Not as bad a drawing as I remember it being. XD